The Chinese Remainder Theorem for Strongly Semisimple MV-Algebras and Lattice-Groups

摘要

An MV-algebra (equivalently, a lattice-ordered Abelian group with adistinguished order unit) is strongly semisimple if all of its quotients modulofinitely generated congruences are semisimple. All MV-algebras satisfy aChinese Reminder Theorem, as was first shown by Keimel four decades ago in thecontext of lattice-groups. In this note we prove that the Chinese RemainderTheorem admits a considerable strengthening for strongly semisimple structures.